understand you to have done) that our belief in the Laws of Nature is based upon the Imagination, you virtually conceded the validity of a kind of proof in which faith and hope play a large part, and in which demonstration is impossible. "Demonstration" applies to mathematics and to syllogisms where the premises are granted, though it is also sometimes loosely used of proof conveyed by personal observation; "proof" applies to the other affairs of life. Demonstration appeals very largely (not entirely, as I have shown above, but very largely) to Reason; proof is largely based on Faith. Having defined "angles," "triangles," "base," and "isosceles," and having been granted certain axioms and postulates, I can demonstrate that the angles at the basis of an isosceles triangle are equal to one another; but I cannot "demonstrate" that, if I throw a stone in the air, it will come down again, though I am perfectly convinced that it will come down, and though I commonly assert that I can "prove" that it will come down.
Why, your whole life is full of beliefs—as certain as any beliefs can be—which it is impossible to demonstrate! When you got up this morning did you not believe that your razor would shave and your looking-glass reflect; that your boiling water would scald if you spilt it, and your egg break if you dropped it; and a score or two of other similar perfectly certain beliefs—all entertained and acted on in less than an hour, but all incapable of demonstration? But you maintain perhaps that "these beliefs are not beliefs, but knowledge based on the uniformity of the laws of nature; you know that the laws of nature are uniform, and therefore you knew that your razor would shave." But how, I ask, do you know that the laws of nature are uniform? "By the experience of mankind during many thousands of years." But how do you know that what has been in the past will be in the future—will
